Patent application DE 10 2004 061 810 A1 discloses a piston pump with a stepped piston with stepped diameter, which is axially movable inside a pump bore also with stepped diameter. The pump bore need not be produced by boring, but may in principle be produced in any manner. To drive the stepped piston in a reciprocating stroke motion in the pump bore, the known piston pump has a cam which is arranged on an end face of the stepped piston on the cam side, and on the periphery of which an end face of the stepped piston rests. On an end face remote from the cam—which is here designated the displacement side for the sake of clarity—the stepped piston of the known piston pump delimits a displacement chamber in the pump bore, the volume of which alternately reduces and enlarges on a reciprocating stroke movement of the stepped piston. The piston stroke during which the volume of the displacement chamber reduces is here designated the forward stroke, and the stroke in the opposite direction during which the volume of the displacement chamber enlarges is here designated the return stroke. The stepped piston of the known piston pump has a ring step facing away from the displacement chamber and delimiting a chamber in the pump bore, which is here referred to as a step chamber for the sake of clarity. A volume change of the step chamber is the opposite of the volume change of the displacement chamber; the volume of the step chamber enlarges on the forward stroke of the stepped piston and reduces on the return stroke. The step chamber of the known piston pump is an annular chamber surrounding the stepped piston in the pump bore, the cross-section of which is smaller than a cross-section of the displacement chamber, so that the volume change of the step chamber opposite to that of the displacement chamber on the stroke movement of the stepped piston is smaller. The step chamber and the displacement chamber communicate with a pump outlet. On a forward stroke, the stepped piston of the known piston pump displaces fluid from the displacement chamber into the pump outlet, and sucks fluid into the step chamber from the pump outlet. Because the volume change of the displacement chamber is greater than the volume change of the step chamber, on a forward stroke the piston pump displaces fluid from the pump bore into the pump outlet. On the return stroke, the known piston pump sucks in fluid from a pump inlet through an inlet valve into the displacement chamber, the volume of which enlarges on the return stroke, and displaces fluid from the step chamber into the pump outlet. The known piston pump therefore has the advantage that it displaces fluid into the pump outlet on both the forward stroke and on the return stroke, whereby a fluid volume flow in the pump outlet is more even and pressure pulsations are smaller. Ideally, the displacement chamber and the step chamber have cross-section ratios of 2:1, so that the piston pump displaces the same amount of fluid into the pump outlet on both strokes.